We devise and experiment with a dynamical kernel-based system for tracking hand movements from neural activity. The state of the system corresponds to the hand location, velocity, and acceleration, while the system's input are the instantaneous spike rates. The system's state dy- namics is defined as a combination of a linear mapping from the previous estimated state and a kernel-based mapping tailored for modeling neural activities. In contrast to generative models, the activity-to-state mapping is learned using discriminative methods by minimizing a noise-robust loss function. We use this approach to predict hand trajectories on the basis of neural activity in motor cortex of behaving monkeys and find that the proposed approach is more accurate than both a static approach based on support vector regression and the Kalman filter. The paper focuses on the problem of tracking hand movements, which constitute smooth spatial trajectories, from spike trains of a neural population. We do so by devising a dynam- ical system which employs a tailored kernel for spike trains along with a linear mapping corresponding to the states' dynamics.

This paper proposes a method for computing fast approximations to sup- port vector decision functions in the field of object detection. In the present approach we are building on an existing algorithm where the set of support vectors is replaced by a smaller, so-called reduced set of syn- thesized input space points. In contrast to the existing method that finds the reduced set via unconstrained optimization, we impose a structural constraint on the synthetic points such that the resulting approximations can be evaluated via separable filters. For applications that require scan- ning large images, this decreases the computational complexity by a sig- nificant amount. Experimental results show that in face detection, rank deficient approximations are 4 to 6 times faster than unconstrained re- duced set systems.

We establish learning rates to the Bayes risk for support vector machines (SVMs) with hinge loss. In particular, for SVMs with Gaussian RBF kernels we propose a geometric condition for distributions which can be used to determine approximation properties of these kernels. Finally, we compare our methods with a recent paper of G. Blanchard et al..

We describe an algorithm for support vector machines (SVM) that can be parallelized efficiently and scales to very large problems with hundreds of thousands of training vectors. Instead of analyzing the whole training set in one optimization step, the data are split into subsets and optimized separately with multiple SVMs. The partial results are combined and filtered again in a'Cascade' of SVMs, until the global optimum is reached. The Cascade SVM can be spread over multiple processors with minimal communication overhead and requires far less memory, since the kernel matrices are much smaller than for a regular SVM. Convergence to the global optimum is guaranteed with multiple passes through the Cascade, but already a single pass provides good generalization.

We consider the problem of deriving class-size independent generaliza- tion bounds for some regularized discriminative multi-category classi- fication methods. In particular, we obtain an expected generalization bound for a standard formulation of multi-category support vector ma- chines. Based on the theoretical result, we argue that the formula- tion over-penalizes misclassification error, which in theory may lead to poor generalization performance. A remedy, based on a generalization of multi-category logistic regression (conditional maximum entropy), is then proposed, and its theoretical properties are examined.

Motivated by the particular problems involved in communicating with "locked-in" paralysed patients, we aim to develop a brain- computer interface that uses auditory stimuli. We describe a paradigm that allows a user to make a binary decision by focusing attention on one of two concurrent auditory stimulus sequences. Using Support Vector Machine classification and Recursive Chan- nel Elimination on the independent components of averaged event- related potentials, we show that an untrained user's EEG data can be classified with an encouragingly high level of accuracy. This suggests that it is possible for users to modulate EEG signals in a single trial by the conscious direction of attention, well enough to be useful in BCI.

An analog system-on-chip for kernel-based pattern classification and se- quence estimation is presented. State transition probabilities conditioned on input data are generated by an integrated support vector machine. Dot product based kernels and support vector coefficients are implemented in analog programmable floating gate translinear circuits, and probabil- ities are propagated and normalized using sub-threshold current-mode circuits. A 14-input, 24-state, and 720-support vector forward decod- ing kernel machine is integrated on a 3mm3mm chip in 0.5m CMOS technology. Experiments with the processor trained for speaker verifica- tion and phoneme sequence estimation demonstrate real-time recognition accuracy at par with floating-point software, at sub-microwatt power.

We show that anomaly detection can be interpreted as a binary classifi- cation problem. Using this interpretation we propose a support vector machine (SVM) for anomaly detection. We then present some theoret- ical results which include consistency and learning rates. Finally, we experimentally compare our SVM with the standard one-class SVM.

Regularization plays a central role in the analysis of modern data, where non-regularized fitting is likely to lead to over-fitted models, useless for both prediction and interpretation. We consider the design of incremen- tal algorithms which follow paths of regularized solutions, as the regu- larization varies. These approaches often result in methods which are both efficient and highly flexible. We suggest a general path-following algorithm based on second-order approximations, prove that under mild conditions it remains "very close" to the path of optimal solutions and illustrate it with examples. Many commonly used supervised learning methods can be cast in this form, including regularized 1-norm and 2-norm support vector machines [13, 4], regularized linear and logistic regression (i.e.

This paper investigates a new learning model in which the input data is corrupted with noise. We present a general statistical framework to tackle this problem. Based on the statistical reasoning, we propose a novel formulation of support vector classification, which allows uncer- tainty in input data. We derive an intuitive geometric interpretation of the proposed formulation, and develop algorithms to efficiently solve it. Empirical results are included to show that the newly formed method is superior to the standard SVM for problems with noisy input.